ISSN 2394-5125
 

Review Article 


DECOMPOSITION OF PRE A*- ALGEBRA WITH JX

D. Kalyani, J.VenkateswaraRao, B. Vijaya Kumar.

Abstract
This manuscript deals with the decomposition of Pre A*- algebra. It is proved that if A is a Pre A*- algebra and x  A, then the set J_x = {s  A / x ≤ s} is a Pre A*- algebra under the induced operations , where the complementation is defined by s* = x s^~, the relation ≤ (less than or equal to) defined on Pre A*- algebra A by x ≤ s if s  x = x  s = s.If B is a Boolean algebra anda  B, thenthe set (a] = {x  B / x ≤ a} ([a) = {x  B / a ≤ x}) is a Boolean algebra under the induced operations ,  where the complementation is defined by x* = a x^', then we know that B is isomorphic to (a]  [a). Based on this result we prove similar decompositions for a Pre A*- algebra.

Key words: Centre of Pre A*- algebra, Decomposition of Pre A*- algebra, PreA*- algebra, Pre A*- isomorphism.


 
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Pubmed Style

D. Kalyani, J.VenkateswaraRao, B. Vijaya Kumar. DECOMPOSITION OF PRE A*- ALGEBRA WITH JX. JCR. 2020; 7(5): 933-935. doi:10.31838/jcr.07.05.191


Web Style

D. Kalyani, J.VenkateswaraRao, B. Vijaya Kumar. DECOMPOSITION OF PRE A*- ALGEBRA WITH JX. http://www.jcreview.com/?mno=100998 [Access: August 18, 2021]. doi:10.31838/jcr.07.05.191


AMA (American Medical Association) Style

D. Kalyani, J.VenkateswaraRao, B. Vijaya Kumar. DECOMPOSITION OF PRE A*- ALGEBRA WITH JX. JCR. 2020; 7(5): 933-935. doi:10.31838/jcr.07.05.191



Vancouver/ICMJE Style

D. Kalyani, J.VenkateswaraRao, B. Vijaya Kumar. DECOMPOSITION OF PRE A*- ALGEBRA WITH JX. JCR. (2020), [cited August 18, 2021]; 7(5): 933-935. doi:10.31838/jcr.07.05.191



Harvard Style

D. Kalyani, J.VenkateswaraRao, B. Vijaya Kumar (2020) DECOMPOSITION OF PRE A*- ALGEBRA WITH JX. JCR, 7 (5), 933-935. doi:10.31838/jcr.07.05.191



Turabian Style

D. Kalyani, J.VenkateswaraRao, B. Vijaya Kumar. 2020. DECOMPOSITION OF PRE A*- ALGEBRA WITH JX. Journal of Critical Reviews, 7 (5), 933-935. doi:10.31838/jcr.07.05.191



Chicago Style

D. Kalyani, J.VenkateswaraRao, B. Vijaya Kumar. "DECOMPOSITION OF PRE A*- ALGEBRA WITH JX." Journal of Critical Reviews 7 (2020), 933-935. doi:10.31838/jcr.07.05.191



MLA (The Modern Language Association) Style

D. Kalyani, J.VenkateswaraRao, B. Vijaya Kumar. "DECOMPOSITION OF PRE A*- ALGEBRA WITH JX." Journal of Critical Reviews 7.5 (2020), 933-935. Print. doi:10.31838/jcr.07.05.191



APA (American Psychological Association) Style

D. Kalyani, J.VenkateswaraRao, B. Vijaya Kumar (2020) DECOMPOSITION OF PRE A*- ALGEBRA WITH JX. Journal of Critical Reviews, 7 (5), 933-935. doi:10.31838/jcr.07.05.191